We have some people trying to report four places to the right of the decimal with inputs that rounded to 2 and 3 decimal places. Can you please articulate why it is impossible to guarantee four decimal precision? I have been unsuccessful in my attempts and am looking for help from someone with a formal math background. Many thanks in advance.

I don't think there's any hard and fast rule about this. I'd go with 3 dps if the input numbers are exact, probably 2 dps if the inputs are rounded.
(BTW 0.276 not 0.278)